The field of “4- or 5-axis” machining combines the various kinematic machine tool configurations which make it possible to orient the workpiece with respect to the tool with 4 or 5 degrees of freedom, respectively. The 4- or 5-axis machines thus make it possible to machine complex, ruled or warped surfaces by interpolation. The kinematic chain is generally formed by 3 linear axes and 1 or 2 rotational axes for a respectively 4- or 5-axis machine. An example of a 5-axis kinematic configuration is represented in FIG. 1. The tool 1 moves along the three linear axes X, Y and Z, with Z perpendicular to the plane X-Y, and the workpiece 2 moves along the two rotational axes B and C respectively aligned with Y and Z.
The trajectory of the tool is described by the combination of the tool center point (TCP) and of the orientation of the rotational axes of the machine. It is this information which makes up the machining program and defines the path of the tool with respect to the workpiece. What is concerned here is a program in RTCP (rotation tool center point) mode, that is to say that each program line (or program block) is composed of the coordinates XYZ of the path of the tool tip in the frame of reference of the workpiece and of one or two angular coordinates depending on whether work is carried out in four or five axes.
The machining programs are generated with the aid of CADM softwares which allow the pooling of elements defining the application to be processed: geometry of the workpiece and of the tool, kinematic configuration of the machine and machining strategy. It is in particular possible to generate and then visualize the path of the tool on the workpiece.
The tool-tip speed is not a constraining parameter for the generation of the machining program by the CADM. It is generally fixed by the cutting parameters linking the tool and the machined material and is therefore not subject to any constraint linked with the kinematic configuration of the machine on which the program is executed. Thus, maintaining a constant tool-tip advance speed implies that the machine is capable of at any time ensuring the workpiece-tool positioning and the speed which are imposed by the program.
In practice, this latter condition is far from always being observed. For example, when large changes of orientation of the tool are programmed on a small portion of the path of the tool, maintaining the tool-tip advance speed implies dynamic performance levels which the machine cannot always provide. The machine is consequently forced to reduce the tool-tip advance speed so as to comply with the path and the orientation which are imposed by the program.
This phenomenon is illustrated in FIGS. 2a and 2b. It will be noted that the going-around of a small radius defined by the vectors Δx′ and Δz′ on the machined workpiece results in a much greater movement at the axes of the machine, that is to say Δx and Δz. With these movements being carried out at the same time, the speed of the machine axes is thus amplified with respect to the programmed tool-tip speed.
The reason for this amplification is purely geometric. The movement Δx and Δz of the linear axes of the machine results in fact from the superimposition of two movements. The first movement is composed of the trajectory of the tool tip on the component programmed by the CADM and represented in broken line (Δx′ and Δz′). The second movement along the axes X and Y results from the rotation of the component necessary for maintaining the tool-workpiece orientation imposed by the program. This second movement is commonly referred to as “follower” movement. The more the component is off-centered with respect to the axes of rotation of the machine, the greater the amplitude of this follower movement. This observation also applies for the machine configuration of type RTTTR composed of a spindle on axis B and a table on axis C or A.
A second problem encountered in this type of configuration lies in the fact that the CADM systems do not make it possible to anticipate in a controlled manner the speed discontinuities experienced by the axes of the machine when they are subjected to the transitions between the regions machined without rotational axis and those machined therewith.
Starting from the preceding example taken up again in FIG. 3, it will be noted that the two regions of the tool path situated upstream and downstream of the radius can be machined in two linear axes (AL) without intervention of the rotational axes (AR). It is in this way that they are processed by the CADM since the latter limits to a maximum the axes involved in each movement. The speed profile of the axis B resulting from this strategy is represented in FIG. 3. It comprises discontinuities at the start and at the end of the radius (see surrounded regions). They are indeed compatible with the movement simulation generated by the CADM but incompatible with the dynamic performance of the axes of the machine. Specifically, a speed jump is manifested by an acceleration jump which can be complied with only on condition that the available driving force for each axis involved is sufficient. In all cases, these acceleration peaks will have the consequence of subjecting the structures of the machine to inertial forces which are large and therefore incompatible with the level of precision required for the finishing operations, for example. There results the formation of undesirable marks on the workpiece.
This problem of the axis speed discontinuities is directly influenced by the problem explained above. Specifically, the higher the speed to be achieved by the rotational axes on account of the amplification resulting from the follower movements, the higher the speed jump necessary to ensure a constant tool-tip advance speed.
The solution which would consist in reducing the tool-tip advance speed in the program is rarely conceivable since it does not prevent the discontinuities in the speed profiles, it deviates from the optimal cutting conditions and it reduces the productivity of the process.
Other solutions proposed in documents EP 2 336 839, EP 1 235 126 and EP 0 917 033 consist in locally smoothing or softening the speed profile of one or more axes taken independently. These are optimization methods which have the object of modifying the trajectory of the tip of the tool on the passage of a geometric discontinuity. This approach brings into play the notion of error tolerance between the previously programmed nominal trajectory and the softened trajectory resulting from the optimization. The error thus generated is plotted on all the axes taken into account for the reconstruction of the softening trajectory. These solutions indeed make it possible to reduce the discontinuities associated with the axes but in no way take into account the relative position of the various linear or rotational axes of the machine with respect to the workpiece to be machined. In addition, discontinuities on the speeds of the rotational axes can appear in regions where there is not a geometric discontinuity. For example, discontinuities on the speeds of the rotational axes can appear at the junction between a planar portion and a curved portion. In this case, the methods disclosed based on the detection of a geometric discontinuity will not provide solutions. Finally, the aforementioned documents disclose methods of optimization of the programmed trajectory which are applied at the numerical control, which greatly limits the margin of flexibility with respect to a method of optimization applied upstream to the machining program as such. These methods which are applied at the numerical control only allow a very local optimization at the level of the discontinuity.